Dynamic modeling of trolling-mode AFM: Considering effects of cantilever torsion, nanoneedle flexibility and liquid-nanoneedle interactions

Trolling mode atomic force microscope (TR-Mode AFM) significantly reduces the hydrodynamic drag generated during operation in liquid environments. This is achieved by utilizing a long nanoneedle and keeping the cantilever out of liquid. In this research, a continuous mathematical model is developed to study TR-Mode AFM dynamics near a sample submerged in the liquid. Effects of cantilever torsion, nanoneedle flexibility, and liquid-nanoneedle interactions are considered in the model. In order to derive the equations of motion, Hamilton's principle and assumed mode method are used. System operation in dynamic mode is numerically simulated and the accuracy of the results is verified by comparison with the results of the finite element method. Displacements of different components of the system are also compared with each other and the dominant displacements are determined.